Noise, vibration and harshness
Slide 2 of 63 AIM Introduce the basic concepts and importance of vibration theory to vehicle design Consider the role of the designer in vibration control Demonstrate methods for the control of vibration to help the elimination of noise and harshness Indicate methods by which the designer can control vibration and noise to create an equitable driving environment
Slide 3 of 63 Basic concepts Vibration sources are characterized by their time and frequency domain characteristics Categorized principally as Periodic originate from the power unit, ancillaries or transmission simplest form of periodic disturbance is harmonic In the time domain this is represented by a sinusoid and in the frequency domain by a single line spectrum Random disturbances from terrain inputs to wheels only statistical representations are possible commonly represented by its power spectrum
Slide 4 of 63 Basic concepts All mass-elastic systems have natural frequencies For linear system these frequencies are constant related only to the mass and stiffness distribution Non-linear effects require special treatment A few of the lower order frequencies are of interest because the higher ones are more highly damped. For one frequency, a system vibrates in a particular way, depicted by the relative amplitude and phase at various locations - mode of vibration
Slide 5 of 63 Reason for vibration analysis Lightly damped structures can produce high levels of vibration from low level sources if frequency components in the disturbance are close to one of the system s natural frequencies. This means that well designed and manufactured subsystems, which produce low level disturbing forces, can still create problems when assembled on a vehicle. In order to avoid these problems, at the design stage it is necessary to model the system accurately and analyze its response to anticipated disturbances
Slide 6 of 63 Approach to vibration analysis Develop a mathematical model of the system and formulate the equations of motion Analyze the free vibration characteristics (natural frequencies and modes) Analyze the forced vibration response to prescribed disturbances and Investigate methods for controlling undesirable vibration levels if they arise
Slide 7 of 63 Mathematical models Provide the basis of all vibration studies at the design stage. Represent the dynamics of a system by one or more differential equations. Distributed-parameter approach - distributed mass and elasticity of some very simple components such as uniform shafts and plates by partial differential equations. not generally possible to represent typical engineering systems (which tend to be more complicated) in this way. Lumped-parameter approach - a set of discrete mass, elastic and damping elements, resulting in one or more ordinary differential equations. Masses are concentrated at discrete points and are connected together by mass less elastic and damping elements. The number of elements used dictates the accuracy of the model To have just sufficient elements for natural vibration modes and frequencies while avoiding unnecessary computing effort.
Mathematical models Slide 8 of 63
Slide 9 of 56 Formulation of System Equations of motion determined by applying Newton s second law to each free-body For complicated geometry, the equations can be formulated by energy methods Figure from Smith,2002
Slide 10 of 56 System characteristics Equation of motion mx + cx + kx = F(t ). Characteristics taken at free vibration [F(t) =0] x = X cos (ω n t φ) no damping Similar formulation of a SDOF system to obtain response as given by graph A(w) =
Slide 11 of 63 Multi Degree of freedom *M+,x - + *K+,x- =,0- Assuming {x} = {A} e st ([M]s 2 + [K]){A} = {0} The non-trivial solution of these is the characteristic equation (or frequency determinant) Set of roots s 2 i = λ = ω 2 λ i is the i-th eigenvalue and ω i the i-th natural frequency - λ*m]{u} = [K]{u} It is solved using standard procedures used for vibration problems
Slide 12 of 63 Multi Degree of Freedom Viscous Damping In (stable) lightly damped systems the frequency determinant is [M]s 2 + [C]s + [K] = 0 For an n-dof system this produces n complex conjugate roots having negative real parts providing information about the frequency and damping associated with each mode of vibration Damping must be considered in the analysis of response of the system when one or more components of a periodic excitation is at or near to one of the system s natural frequencies
Slide 13 of 63 Multi Degree of Freedom Forced-damped vibration (harmonic) Many of the features of harmonic response analysis of SDOF systems extend to MDOF ones, e.g.: When subjected to harmonic excitation an MDOF system vibrates at the same frequency as the excitation. The displacement amplitudes at each of the degrees of freedom are dependent on the frequency of excitation and The dynamic displacement at each DOF lags behind the excitation The frequency response functions (and hence the frequency responses) are complex if damping is included in the analysis.
Slide 14 of 63 Multi Degree of Freedom Forced damped vibration (random excitation) Random excitation arises particularly from terrain inputs and is important in the analysis and design of vehicle suspensions. Form of excitation is non-deterministic in that its instantaneous value cannot be predicted at some time in the future. Some properties of random functions which can be described statistically. The mean or mean square value can be determined by averaging and the frequency content can be determined from methods based on the Fourier transform (Newlands, 1975).
Slide 15 of 63 Vibration control Control at source Engine firing and reciprocating unbalance combine to produce a complex source of vibration which varies with engine operating conditions Reciprocating unbalance arises at each cylinder because of the fluctuating inertia force associated with the mass at each piston no such thing as perfect balance
Slide 16 of 56 Vibration isolation k* = k(1 + ηi) where k is the dynamic stiffness and η the loss factor mx + k(1 + i)x = m e r 2 sin wt = F f (t ) SDOF vibration isolation model and free-body diagram Up to 1.4 Figure from Smith,2002
Slide 17 of 56 Tuned absorbers useful for reducing vibration levels in those systems in which an excitation frequency is close to or coincides with a natural frequency of the system The principles of undamped and damped tuned absorbers can be understood by outlining first the analysis of the damped absorber Undamped absorber as a special case Figure from Smith,2002
Slide 18 of 63 Tuned absorbers For C = 0 ( undamped) [ideally k 2 -m 2 w 2 =0 ie w 1 = w 2 ] Figure from Smith,2002
Slide 19 of 56 A 1 = K *X 1 / F A 2 = K *X 2 / F Dimensionless numbers With damping Tuned absorbers Wider operating range Reduced fatigue of absorber spring Damped Figure from Smith,2002 Un damped
Untuned viscous dampers Devices consist of an inertia (seismic) mass which is coupled to the original system via some form of damping medium (usually silicone fluid) Not tuned for particular resonance At infinite damping both masses move together as one Models for analyzing the untuned viscous damper Slide 20 of 56 Figure from Smith,2002 Response of an untuned viscous damper (m = 1.0)
Slide 21 of 63 Engine Isolation Fluctuating torque at the crankshaft Shaking forces and moments additional dynamic inertial loads arising from vehicle maneuvering and terrain inputs to the wheels The primary components of engine vibration at idling are integer multiples of engine speed Idle speeds for four cylinder engines range from 8 20 Hz producing dominant frequency components in the range from 16 40 Hz. Since the primary bending mode of passenger cars can be less than 20 Hz it is obvious that it is easy to excite body resonance at idle if engine isolation is not carefully designed The problem isolate the chassis from the excitations and restrain the engine against excessive movement due to the engine torque Select appropriate mounts and position them correctly
Slide 22 of 56 Formulation of the vibration equations Denoting the position of the i- th mount attachment point relative to the powertrain in the equilibrium position as r r i 0 (in chassis coordinates) and the translation and rotation of the powertrain relative to the chassis axes as r G and Θ, the deflection of the mount is given by d ci = r i ri 0 ρ i is the location of the mount attachment point relative to the powertrain axes Figure from Smith,2002
Slide 23 of 63 Formulation of the vibration equations The elastic potential energy for a set of mounts typically having orthogonal complex stiffness components represented by the diagonal stiffness matrix [km] i is For chassis
Slide 24 of 63 Formulation of the vibration equations Is a non-diagonal matrix Kinetic energy of the system is {h} G is the momentum denoted by
Slide 25 of 63 Formulation of the vibration equations [M], the symmetrical mass/inertia matrix, is of the form Lagragne s Equations
Slide 26 of 63 Mount requirements and types a low spring rate and high damping during idling and a high spring rate and low damping for high speeds, manoeuvring and when traversing rough terrains.
Slide 27 of 63 Mounting types [1/4] Simple rubber engine mounts These are the least costly and least effective forms of mount and clearly do not meet all the conflicting requirements. They do not provide the high levels of damping required at idling speeds.
Slide 28 of 63 Mounting types [2/4] Hydro-elastic mounts These generally contain two elastic reservoirs filled with a hydraulic fluid. Some also contain a gas filled reservoir. This type of mount exploits the feature of mass-augmented dynamic damping which is a form of tuned vibration absorber. In operation there is relative motion across the damper which produces flexure of the rubber component and transfer of fluid between chambers, thereby inducing a change in mount transmissibility. This type of mount has become common in recent years and some examples are given in the literature (Kim et al., 1992; Muller et al., 1996).
Slide 29 of 63 Mounting types [3/4] Semi-active mounts The operation of these mounts is dependent on modifying the magnitude of the forces transmitted through coupling devices. They may be implemented via low-bandwidth low power actuators which are suited to open-loop control. Some forms of hydraulic semi-active (adaptive) mount use low powered actuators to induce changes in mount properties by modifying the hydraulic parameters within the mount. The actuators may then be on off (adaptive) or continously variable (semi-active) types. Considerable effort has been devoted to this type of technology in recent years. Some examples are given in Morishita et al. (1992) and Kim et al. (1993).
Slide 30 of 63 Mounting types [4/4] Active mounts This type of mount requires control of both the magnitude and direction of the actuator force used to adjust the coupling device. High-speed actuators and sensors require having an operating bandwidth to match the frequency spectrum of the disturbance. Power consumption is generally high in order to satisfy the response criteria. Active vibration control is typically implemented by closedloop control. An example of active engine mount modelling and performance is given by Miller et al. (1995).
Slide 31 of 56 Engine mounting system for a fourcylinder diesel engine It comprises two mass carrying mounts (one a hydramount, the other a hydrabush, both passive mounts) and two torque reacting tie bars. The hydramount is linked to the power unit by an aluminium bridge bracket. Both tie bars have a small bush at the power unit end and a large bush at the body end A torque axis engine mounting system (courtesy of Rover Group Ltd) Figure from Smith,2002
Slide 32 of 56 Engine Mounts level isolation for passenger cars. The modern car designs have a trend for lighter car bodies and more power-intensive engines. Such a weight reduction and increased power requirements often have adverse effects on vibratory behavior, greatly increasing the vibration and noise level From Yunhe Yu, 2001
Slide 33 of 56 Elastomeric mounts Since 1930s represented by familiar Voigt model compact, cost-effective maintenance free. and Bonded elastomeric mounts are known to provide more consistent performance and longer life Dynamic stiffness of an elastomeric mount will be greater at higher frequencies due to damping Desirable : specific nonlinear characteristics to obtain constant natural frequency in a broad weight-load range use of materials with high internal damping materials with highly amplitudedependent damping and stiffness From Yunhe Yu, 2001
Slide 34 of 56 Passive hydraulic mounts All hydraulic mounts reported in the literature are conceptually similar but differ in detailed structural design An elastomeric mount capable of supporting the load and acting as a piston to pump the liquid into the button chamber. Two separate chambers for fluid transfer. An orifice or inertia track to generate damping. A fluid medium Sealing between chamber and the outside. Decoupler to permit low amplitude by-pass of the damping. From Yunhe Yu, 2001
Slide 35 of 56 Passive hydraulic mounts Dynamic stiffness of hydraulic mount with simple orifice or inertia track is greater than that of a comparable elastomeric mount Hydraulic mounts greatly increase damping at low frequencies, they also degrade isolation performance at higher frequencies A de-coupler functions as amplitude limited floating piston. It makes hydraulic mount amplitude-dependent at low amplitude displacement From Yunhe Yu, 2001
Slide 36 of 56 Semi-active and active Engine mounts Semi-active control mechanism Hydraulic type Electro-rheological (ER) fluids - increase damping at resonance and reduce the transmissibility for shock excitation Theory : One degree sky-hook system and used for increasing the damping during the low frequency shock excitation Mainly to improve the system performance at the low frequency range From Yunhe Yu, 2001
Slide 37 of 56 Active engine mounts Counteracting dynamic force created by one or more actuators to suppress transmission of system disturbance force Passive mounts used to support engine in event of an actuator failure Classical- hydraulic mount, and an electromagnetic actuator to isolate high frequency vibration Servo-hydraulic Piezo-actuators -high-speed response, but displacement very small and requires suitable mechanism to increase amplitude Model for active elastomeric mount From Yunhe Yu, 2001 Model for active hydraulic mount
Slide 38 of 56 Active engine mounts The active mount stiffness is equivalent to the stiffness of the passive mount at every frequency except where engine vibration occurs At the disturbance frequency, a tonal controller commands the mount to be very soft Active hydraulic mounts achieve adequate damping at engine bounce frequency and have very low dynamic stiffness at higher frequency considered to be the next generation of engine mounts Dynamic stiffness of an active elastomeric mount From Yunhe Yu, 2001 Dynamic stiffness of hydraulic active mount
Slide 39 of 56 Crankshaft damping Torsional dynamics of crankshafts dependent on the distribution of their mass and elasticity and the excitations arising from the torque/cylinder Because the torque contains a number of harmonic components and engine speed is variable there is a tendency to excite a large number of Torsional resonances as illustrated by the waterfall plot (Torsional amplitude plotted as a function frequency for a range of engine speeds) Waterfall plot for a multi-cylinder engine (courtesy of Simpson International (UK) Ltd) Figure from Smith,2002
Determination of the mass-elastic model Slide 40 of 56 Modal analysis of the mass-elastic model Equivalent model based on first mode of the mass-elastic model Mass-elastic model and first torsion mode of a six cylinder engine Figure from Smith,2002
Slide 41 of 63 Fundamentals of acoustics General sound propagation In an automotive context this is the surrounding air or the vehicle body structure, giving rise to the term structure-borne sound. Produces a propagating (travelling) wave which has a characteristic velocity c, the velocity of sound in air. At some arbitrary point on the path, the air undergoes pressure fluctuations which are superimposed on the ambient pressure. A sound source vibrating at a frequency f, produces sound at this frequency. The distance between pressure peaks is constant and known as the wavelength λ. This is related to c and f by the equation:
Slide 42 of 56 Fundamentals of acoustics Plane wave propagation Wave motion are most easily understood by considering the propagation of a plane wave Table from Smith,2002 Elastic deformation
Slide 43 of 56 Plane wave propagation Specific acoustic impedance, Z The impedance which a propagating medium offers to the flow of acoustic energy is called the acoustic impedance. It is defined as the ratio of acoustic pressure p to the velocity of propagation u. It can be shown (Reynolds, 1981) that Acoustic intensity, I This is defined as the time averaged rate of transport of acoustic energy by a wave per unit area normal to the wavefront. It is given by Reynolds (1981)
Slide 44 of 63 Spherical wave propagation, acoustic near and far fields Spherical waves more closely approximate true source waves, but approximate to plane waves at large distances from a source. It may be shown (Reynolds, 1981) that the wave equation in spherical coordinates is
Slide 45 of 63 Spherical wave propagation, acoustic General solution is near and far fields At large distances from the source (kr >> 1 or r >> λ/2π), z ρ c. [k wave number = w/c; z impedance] Then pressure and particle velocity are in phase and we are in what is called the acoustic far field where spherical wave-fronts approximate to those of plane waves and pressure and velocity are in phase.
Slide 46 of 63 Spherical wave propagation, acoustic near and far fields At distances close to the source (kr << 1 or r << λ/2π), z iρckr. Then pressure and velocity are 90 out of phase and we are in what is called the acoustic near field. The transition from near to far field is in reality a gradual one, but is normally assumed to take place in the vicinity of λ/2 π. For a harmonic wave at 1 khz (λ 1 khz), r = 50 mm; while at 20 Hz; r = 2.5 m. The far field/near field transition has important implications for microphone positioning in sound level measurements
Acoustic quantities expressed in decibel form Slide 47 of 63 Sound Power, Intensity and Pressure levels
Acoustic quantities expressed in decibel form Slide 48 of 63 When it is noted that the threshold of hearing corresponds to a sound pressure level of 0 db it may be shown (Reynolds, 1981) that for normal temperature and pressure (101.3 kpa and 20 C). L W, L I and L p are related as follows
Slide 49 of 56 Effects of reflecting surfaces on sound When an incident wave strikes a reflecting surface the wave is reflected backwards towards the source. In the vicinity of the reflecting surface the incident and reflected waves interact to produce what is known as a reverberant field propagation Figure from Smith,2002 Sound pressure level as a function of distance from a simple spherical source
Slide 50 of 63 Effects of reflecting surfaces on sound propagation If the sound source is next to a hard reflecting surface, four idealized cases -- whole space radiation when there are no reflecting surfaces, i.e. the source is in free space, half-space radiation when the source is positioned at the centre of a flat hard (reflecting) surface quarter space radiation when the source is positioned at the intersection of two flat hard surfaces which are perpendicular to one another eighth space radiation when the source is positioned at the intersection of three flat perpendicular hard surfaces. In each case there is an increase in acoustic intensity. The effect can be described by the directivity index DI in terms of the directivity factor Q. DI = 10 log10 Q db
Slide 51 of 56 Human response to sound The frequency range extends from 20 Hz to 20 khz and the SPL extends from the threshold of hearing at the lowest boundary to the threshold of feeling (pain) at the highest Human ear is most sensitive between 500 Hz and 5 khz and is insensitive to sounds below 100 Hz The audible range Figure from Smith,2002
Slide 52 of 56 Sound measurement Sound level meters The most basic instrument for sound measurement is a sound level meter comprising a microphone, r.m.s. detector with fast and slow time constants. A-weighting network to enable measurements to be made which relate to human response to noise, leading to so called A weighted noise levels LpA, expressed in db(a). Because of the frequency sensitivity of the human ear, the A-weighting network has the form shown in Figure The A-weighting curve Figure from Smith,2002
Slide 53 of 63 Frequency analysers Since the frequency spectrum of noise is closely related to the origins of its production, frequency analysis is a powerful tool for identifying noise sources and enables the effectiveness of noise control measures to be assessed Narrow band frequency analyzers are a necessity. Simultaneous filtering in multiple narrow band filters
Slide 54 of 56 Drive-by noise tests (ISO 362, 1981) The procedure is to accelerate the vehicle in a prescribed way and in a prescribed gear past a microphone set up at a height of 1.2 m above a hard reflecting surface and 7.5 m from the path of the vehicle When the vehicle reaches A the throttle should be opened fully and maintained in this position until the rear of the vehicle reaches B
Slide 55 of 63 Noise from stationary vehicles Vehicles in the vicinity of the exhaust silencer (ISO 5130, 1978) Engine running at 75% of the speed at which it develops maximum power For these measurements, the exhaust outlet and microphone are in the same horizontal plane with the microphone 500 mm from the exhaust outlet and at an axis of 45 to it. The background noise level is also measured and the maximum difference between the vehicle noise and the background noise is then compared with vehicle s specified noise level
Slide 56 of 63 Interior Noise No legal requirements Assessed by experienced assesors Ad Hoc Criterion like Articulation Index used 200 Hz to 16kHz split into 16 bands SPL is measured in each band
Slide 57 of 63 Interior noise in vehicles Articulation index ( by Greaves) Where, A 0 = SPL for zero intelligibility of conversation A 100 = SPL for 100% intelligibility W f = weighting factor for each third octave band Overall AI is measured by adding together 16 different indices
Slide 58 of 63 Engine noise Engine noise originates from both the combustion process and mechanical forces associated with engine dynamics Noise control: Controlling pressure variations Piston slap mass of piston, gudgeon pin design, offset Noise shields Crankshaft spoked, damper
Slide 59 of 63 Transmission noise Misalignment of shafts, single tooth incorrectly cut or damaged. f s1, f s2 = f tm ± f ss f ss shaft speed frequency Correct standard tooth profiles to account for tooth elasticity effects But gear teeth are subjected to variable loading, it is impossible to correct for all eventualities
Slide 60 of 63 INTAKE NOISE Generated by interruption of airflow at inlet valves Transmitted via air cleaner Radiated by air duct Noise of 10-15 db Turbo charger compressor noise also radiated from the air duct At blade passing frequency (also higher harmonics) Typically 2-4 khz
Slide 61 of 63 EXHAUST NOISE Produced by release of gases as exhaust valves open and close F = engine speed /60 * number of cyls / 2 Vary with engine load (upto 15 db) Turbo charging reduces engine and exhaust noise (because of better combustion)
Attenuation of intake and exhaust noise Slide 62 of 63 Devices which minimize flow of sound waves Allow gas flow Called acoustic filters Two types Dissipative (absorb acoustic energy) Reactive (by intereference)
Slide 63 of 56 Intake and exhaust noise Dissipative silencers absorptive material which absorbs acoustic energy from the gas flow Produces attenuation at f>500hz Reactive silencers when the sound in a pipe or duct encounters a discontinuity in the cross-section, some of the acoustic energy is reflected back creating destructive interference Suitable for attenuating low frequency noise Causes pressure loss Figure from Smith,2002
Slide 64 of 56 The Helmholtz resonator Incorporated in the air filter f c 2 A LV Produces low frequency resonance, and Attenuation at higher frequencies
Slide 65 of 63 Catalytic Convertors Fitted immediately after exhaust manifold For quick heating needed for their functioning Have an acoustic attenuation effect Gas passes through narrow ceramic pipes Attenuation as well as dispersion Silencers downstream of catalytic convertors Have an acoustic resonant frequency Tuned to avoid exciting structural frequencies Hence, Often have a double skin and insulation AND Isolated from vehicle body by suspending it from flexible systems
Slide 66 of 63 Intake and exhaust noise The following are some of the devices used to overcome specific silencer tuning problems. The Helmholtz resonator a through-flow resonator which amplifies sound at its resonant frequency, but attenuates it outside this range. Circumferential pipe perforations create many small sound sources resulting in a broadband filtering effect due to increased local turbulence. Venturi nozzles designed to have flow velocities below the speed of sound, they are used to attenuate low frequency sound.
Slide 67 of 63 Aerodynamic noise For road vehicles this can be broken down into three noise generating components: Boundary layer distributed over the vehicle body Boundary layer noise tends to be random in character Absorbent materials Edge effects noise level higher than boundary layer noise Caused by vortices formed at edges Vortex shedding (large vortices roll up and break into smaller ones) at various locations on the vehicle body and also at cooling fans
Slide 68 of 63 Minimizing Aerodynamic noise minimizing protrusions from the body surface, making the body surface smooth and continuous and ensuring that gaps around apertures such as doors are well sealed. Vortices produced at windscreen pillars very little which can be done to improve as aerodynamics at A-pillar contradicts visibility requirements Wing mirrors and wheel trims also cause vortices SU f d where S is the Strouhal Number (based on geometry), U is speed of air, d obstruction dia f = 640 Hz, for d=10 at 70mph inlet and outlet apertures are carefully sited and designed Should not generate noise and noise from engine compartment should not be transmitted to the occupant
Noise from the cooling fan Blades shed helical trailing vortices Result in periodic pressure fluctuations when they strike obstacles fan rotors are made with unevenly spaced blades and with an odd numbers of blades Slide 69 of 63
Slide 70 of 63 Tire noise Two sources of noise Tread pattern excited noise (affected by tire design) Road surface excited noise Tire designers reduce tire noise Chassis designers reduce transmission to occupant The mechanism of tire noise generation is due to an energy release when a small block of tread is released from the trailing edge of the tire footprint and returns to its undeformed position. Tread patterns designed to control frequencies Models of tires with structural dynamic characteristics and the air contained within them are used at the design stage.
Slide 71 of 63 Brake noise Mechanism of noise generation in disc and drum brakes is still not fully understood Complex system of linkages Elements of large area held in contact with hydraulic / friction loading Ad hoc / empirical solutions often used For low frequency drum brake noise Add either a single mass or a combined mass and a visco-elastic layer applied at anti-nodes of the drum back plate (Fieldhouse et al., 1996). At higher frequencies a redistribution of drum mass to eliminate some of the specific back plate vibration modes.